NUMERICAL STUDY OF MULTISCALE CAVITATING FLOW AROUND A HYDROFOIL
-
摘要: 空化的多尺度效应是一种涉及连续介质尺度、微尺度空化泡以及不同尺度间相互转化的复杂水动力学现象, 跨尺度模型的构建是解析该多尺度现象的关键. 本文基于欧拉-拉格朗日联合算法, 通过界面捕捉法求解欧拉体系下大尺度空穴演化, 通过拉格朗日体系下离散空泡模型求解亚网格尺度离散空泡的运动及生长溃灭. 同时, 通过判断空泡与网格尺度间的关系判定不同尺度空化泡的求解模型. 基于建立的多尺度算法对绕NACA66水翼空化流动进行模拟, 将数值结果与实验进行对比, 验证了数值计算方法的准确性. 研究结果表明, 离散空泡数量与空化发展阶段密切相关, 在附着型片状空穴生长阶段, 离散空泡数量波动较小, 离散空泡主要分布在气液交界面位置; 在回射流发展阶段, 离散空泡逐渐增加并分布在回射流扰动区; 在云状空穴溃灭阶段, 离散空泡数量增多且主要分布在气液掺混剧烈的空化云团溃灭区. 在各空化发展阶段, 离散空泡直径概率密度函数均符合伽玛分布. 空化湍流流场特性对拉格朗日空泡空间分布具有重要影响, 离散空泡主要分布在强湍脉动区、旋涡及回射流发展区域.Abstract: The multiscale effect of cavitation is a complex hydrodynamic phenomenon involving macroscale cavitation, microscale cavitation bubbles and transformation between scales. The cavitating flow around a NACA66 hydrofoil is simulated based on the established Euler-Lagrange algorithm. The macroscale cavitation vapor was captured through a large eddy simulation (LES) method and the volume of fluid (VOF) method in an Eulerian analysis. The motion, growth and collapse of sub-grid scale discrete bubbles were solved through discrete bubble model (DBM) in Lagrangian frame. Meanwhile, the solution model of different scale cavitation is selected through the comparison of scale between cavitation cavity and the local grid. The experimental results are compared with the numerical results to verify the accuracy of the numerical method. The results show that the number of discrete bubbles is closely related to the development of cloud cavitation. The number of discrete bubbles fluctuate little in the growth stage of attached sheet cavity with the bubbles mainly distributed at the interface of water and vapour. With the re-entrant jet occur at the trailing edge of attached cavity and develop to leading edgy of hydrofoil, the bubble number gradually increase and fill up the jet disturbance region. When the cavity detach, converge and shed downstream along with the hydrofoil, the discrete bubble number increase rapidly and the bubbles dispersed in the mixing region of water and vapour. Moreover, the probability density function of discrete bubble diameter conforms to Gamma distribution for the whole stage of cloud cavitation. With the increase of cavitation diameter, the number of cavitation first increases and then decreases. Additionally, the characteristics of the cavitation turbulent flow field have an important influence on the distribution of bubbles, and the discrete bubble is mainly distributed in the region of strong turbulence intensity, vortex and re-entrant flow.
-
Key words:
- cavitation /
- multiscale /
- Euler-Lagrange /
- interface capturing method /
- discrete bubble model
-
表 1 网格数、
$x^+ $ 及$z^+ $ 值Table 1. Number of grids, x+ and
$z^+$ valuesGrid number/106 x + z + MeshⅠ 2.35 220 52 MeshⅡ 4.7 89 22.5 Mesh Ⅲ 6.7 75 16 -
[1] Wang GY, Senocak I, Shyy W, et al. Dynamics of attached turbulent cavitating flows. Progress in Aerospace Sciences, 2001, 37(6): 551-581 doi: 10.1016/S0376-0421(01)00014-8 [2] Li LM, Huo YK, Wang ZD, et al. Large eddy simulation of tip-leakage cavitating flow using a multiscale cavitation model and investigation on model parameters. Physics of Fluids, 2021, 33: 092104 doi: 10.1063/5.0060590 [3] Wu WB, Liu YL, Zhang AM, et al. Numerical investigation on underwater explosion cavitation characteristics near water wave. Ocean Engineering, 2020, 205: 107321 doi: 10.1016/j.oceaneng.2020.107321 [4] Yang J, Xie T, Liu XH, et al. Study of unforced unsteadiness in centrifugal pump at partial flow rates. Journal of Thermal Science, 2021, 30: 88-99 doi: 10.1007/s11630-019-1241-2 [5] 王巍, 张庆典, 唐滔等. 射流对绕水翼云空化流动抑制机理研究. 力学学报, 2020, 52(1): 12-23 (Wang Wei, Zhang Qingdian, Tang Tao, et al. Mechanism investigation of water injection on suppressing hydrofoil cloud cavitation flow. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 12-23 (in Chinese) doi: 10.6052/0459-1879-19-282Wang Wei, Zhang Qingdian, Tang Tao, et al. Mechanism investigation of water injection on suppressing hydrofoil cloud cavitation flow. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 12-23 (in Chinese) doi: 10.6052/0459-1879-19-282 [6] Wang ZH, Zhang B. In-situ study on cavitation erosion behavior of super ferritic stainless steel. Wear, 2021, 482-483: 203986 doi: 10.1016/j.wear.2021.203986 [7] Wu PF, Wang XM, Lin WJ, et al. Acoustic characterization of cavitation intensity: A review. Ultrasonics Sonochemistry, 2022, 82: 105878 doi: 10.1016/j.ultsonch.2021.105878 [8] 王畅畅, 王国玉, 黄彪等. 可压缩空化流动空穴演化及压力脉动特性实验研究. 力学学报, 2019, 51(5): 1296-1309 (Wang Changchang, Wang Guoyu, Huang Biao, et al. Experimental investigation of cavitation characteristics and dynamics in compressible turbulent cavitating flows. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1296-1309 (in Chinese) doi: 10.6052/0459-1879-19-128Wang Changchang, Wang Guoyu, Huang Biao, et al. Experimental investigation of cavitation characteristics and dynamics in compressible turbulent cavitating flows. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1296-1309 (in Chinese) doi: 10.6052/0459-1879-19-128 [9] 高远, 黄彪, 吴钦等. 绕水翼空化流动及振动特性的实验研究. 力学学报, 2015, 47(6): 1009-1016 (Gao Yuan, Huang Biao, Wu Qin, et al. Experimental investigation of the vibration characteristics of hydrofoil in cavitating flow. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6): 1009-1016 (in Chinese) doi: 10.6052/0459-1879-15-173Gao Yuan, Huang Biao, Wu Qin, et al. Experimental investigation of the vibration characteristics of hydrofoil in cavitating flow. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6): 1009-1016 (in Chinese) doi: 10.6052/0459-1879-15-173 [10] Tsuru W, Konishi T, Watanabe S, et al. Observation of inception of sheet cavitation from free nuclei. Journal of Thermal Science, 2017, 26: 223-228 doi: 10.1007/s11630-017-0933-8 [11] Khoo MT, Venning JA, Pearce BW, et al. Statistical aspects of tip vortex cavitation inception and desinence in a nuclei deplete flow. Experiments in Fluids, 2020, 61: 145-158 doi: 10.1007/s00348-020-02967-x [12] Stutz B, Reboud JL. Measurements within unsteady cavitation. Experiments in Fluids, 2000, 29: 545-552 doi: 10.1007/s003480000122 [13] Kubota A, Kato H, Yamaguchi H, et al. Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique. Journal of Fluids Engineering, 1989, 111: 204-210 doi: 10.1115/1.3243624 [14] Kawanami Y, Kato H, Yamauchi H, et al. , Mechanism and control of cloud cavitation. Journal of Fluids Engineering, 1997, 119(4): 788-794 doi: 10.1115/1.2819499 [15] Maeda M, Yamaguchi H, Kato H. Laser holography measurement of bubble population in cavitation cloud on a foil section//1st Joint ASME/JSME Fluid Engineering Conference, Portland, FED, 1991, 116: 67-75 [16] Wu Q, Huang B, Wang GY, et al, The transient characteristics of cloud cavitating flow over a flexible hydrofoil. International Journal of Multiphase Flow, 2018, 99: 162-173 [17] Huang B, Young YL, Wang G, et al. Combined experimental and computational investigation of unsteady structure of sheet/cloud cavitation. Journal of Fluids Engineering, 2013, 135(7): 071301 doi: 10.1115/1.4023650 [18] 程怀玉, 季斌, 龙新平等. 空化对叶顶间隙泄漏涡演变特性及特征参数影响的大涡模拟研究. 力学学报, 2021, 53(5): 1268-1287Cheng Huaiyu, Ji Bin, Long Xinping, et al. LES investigation on the influence of cavitation on the evolution and characteristics of tip leakage vortex. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1268-1287 (in Chinese) [19] 谢庆墨, 陈亮, 张桂勇等. 基于动力学模态分解法的绕水翼非定常空化流场演化分析. 力学学报, 2020, 52(4): 1045-1054Xie Qingmo, Chen Liang, Zhang Guiyong, et al. Analysis of unsteady cavitation flow over hydrofoil based on dynamic mode decomposition. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1045-1054 (in Chinese) [20] Tomar G, Fuster D, Zaleski S, et al. Multiscale simulations of primary atomization. Computers & Fluids, 2010, 39(10): 1864-1874 [21] Hsiao CT, Ma J, Chahine GL. Multiscale two-phase flow modeling of sheet and cloud cavitation. International Journal of Multiphase Flow, 2017, 90: 102-117 doi: 10.1016/j.ijmultiphaseflow.2016.12.007 [22] Li LM, Wang ZD, Li XJ, et al. Very Large eddy simulation of cavitation from inception to sheet/cloud regimes by a multiscale model. China Ocean Engineering, 2021, 35(3): 361-371 doi: 10.1007/s13344-021-0033-0 [23] Li LM, Wang ZD, Li XJ, et al. Multiscale modeling of tip-leakage cavitating flows by a combined volume of fluid and discrete bubble model. Physics of Fluids, 2021, 33: 062104 doi: 10.1063/5.0054795 [24] Ebrahim G, Ström H, Bensow RE. Numerical simulation and analysis of multi-scale cavitating flows. Journal of Fluid Mechanics, 2021, 922(A22): 1-54 [25] Wang ZY, Cheng HY, Ji B. Euler–Lagrange study of cavitating turbulent flow around a hydrofoil. Physics of Fluids, 2021, 33: 112108 doi: 10.1063/5.0070312 [26] Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. Journal of Computational Physics, 1992, 100(2): 335-354 doi: 10.1016/0021-9991(92)90240-Y [27] Nicoud F, Ducros F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbulence and Combustion, 1999, 62(3): 183-200 doi: 10.1023/A:1009995426001 [28] Foeth EJ, Terwisga TV, Doorne CV. On the collapse structure of an attached cavity on a three-dimensional hydrofoil. Journal of Fluid Eengineering, 2008, 130(7): 071303 doi: 10.1115/1.2928345 [29] Morsi SA, Alexander AJ. An investigation of particle trajectories in two-phase flow systems. Journal of Fluid Mechanics, 1972, 55(2): 193-208 doi: 10.1017/S0022112072001806 [30] Wang ZD, Li LM, Li XJ, et al. Large eddy simulation of cavitating flow around a twist hydrofoil and investigation on force element evolution using a multiscale cavitation model, Physics of Fluids, 2022, 34: 023303 [31] Blake FG. Bjerknes forces in stationary sound fields. Journal of the Acoustical Society of America, 1949, 21(5): 551 [32] Zwart PJ, Gerber AG, Belamri T, A two-phase flow model for predicting cavitation dynamics//Proceedings of Fifth International Conference on Multiphase Flow, Yokohama, Japan, 2004. [33] Chesters AK. Modelling of coalescence processes in fluid-liquid dispersions: A review of current understanding. Chemical Engineering Research and Design. 1991, 69: 59-70 [34] Kamp AM, Chesters AK, Colin C. Bubble coalescence in turbulent flows: a mechanistic model for turbulence-induced coalescence applied to microgravity bubbly pipe flow. International Journal of Multiphase Flow, 2001, 27(8): 1363-1396 doi: 10.1016/S0301-9322(01)00010-6 [35] Lau YM, Bai W, Deen NG. Numerical study of bubble break-up in bubbly flows using a deterministic Euler –Lagrange framework. Chemical Engineering Science, 2014, 108(28): 9-22 [36] Giannadakis E, Gavaises M, Arcoumanis C. Modelling of cavitation in diesel injector nozzles. Journal of Fluid Mechanics. 2008, 616(10): 153-193 [37] Li LM, Ding WY, Xue FF, et al. Multiscale mathematical model with discrete–continuum transition for gas–liquid–slag three-phase flow in gas-stirred ladles. JOM, 2018, 70(12): 2900-2908 doi: 10.1007/s11837-018-3116-5 [38] Yang RY, Zou RP, Yu AB. Computer simulation of packing of fine particles. Physical Review E, 2000, 62(3): 3900-3908 doi: 10.1103/PhysRevE.62.3900 [39] Li LM, Li BK, Liu ZQ. Modeling of spout-fluidized beds and investigation of drag closures using OpenFOAM. Powder Technology, 2017, 305: 364-376 doi: 10.1016/j.powtec.2016.10.005 [40] Davidson L. Large eddy simulations: How to evaluate resolution. International Journal of Heat and Fluid Flow, 2009, 30(5): 1016-1025 doi: 10.1016/j.ijheatfluidflow.2009.06.006 [41] Yu XM, Hendrickson K, Yue DKP. Scale separation and dependence of entrainment bubble-size distribution in free-surface turbulence. Journal of Fluid Mechanics, 2020, 885(R2): 1-12 [42] Brocchini M, Peregrine DH. The dynamics of strong turbulence at free surfaces. Part 1. Description. Journal of Fluid Mechanics, 2001, 449(25): 225-254 -